Question

The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Question 2 options: 7 m 8 m 14 m 15 m

Answer 1

h=6+b
a=(1/2)bh
a=56

56=(1/2)bh
times 2 both sides
112=bh
h=6+b

112=b(6+b)

112=b²+6b

minus 112 both sides

0=b²+6b-112

factor

what 2 numbers multily to get -112 and add to get 6

-8 and 14

0=(b-8)(b+14)

set to zero

b-8=0

b=8

b+14=0

b=-14

false, measures can't be negative

base=8

h=6+b

h=6+8

h=14

height=14

base=8

Answer 2

Use the formula for the area of a triangle. The length of the base will be 8 metres.

Given,

The area of triangle is 56 square meter.

Let the length of base be x meter.

So, the height of the triangle will be x+6 meters.

We have to calculate the length of the base.

How to get the area of a triangle?

We know that Area of triangle is,

$A=\dfrac{1}{2} \times Base\times Height$

$56=\dfrac{1}{2}\times x\times (x+6)$

$112=x^{2} +6x$

$x^{2} +6x-112=0$

How to solve a quadratic equation?

On solving the above quadratic equation by middle term split method we get,

$x^{2} +14x-8x-112=0$

$x(x+14)-8(x+14)=0$

$(x+14)(x-8)=0$

When

$x+14=0$

$x=-14$

And when

$x-8=0$

$x=8$

Since side cannot be negative so neglecting the negative value of x, the final value of x will be 8.

Hence the correct option is B. 8 meter.

For more details about triangles, follow the link:

https://brainly.com/question/15442893